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Journal of Physics B Atomic Molecular and Optical Physics

Pulse shape control of the spectrum emitted by a two level atom

ANTONINO DI PIAZZA, Emilio Fiordilino, Marvin H. Mittleman

Published Sep 12, 2001• 14 citations
Publisher

Abstract

We find an approximated analytic expression of the acceleration spectrum of a quasi-degenerate two level atom in an external laser field with a non-constant pulse shape function. The spectrum contains odd harmonics and side bands of even harmonics. We show that the relative amplitude of these lines can be controlled by using different rise times of the laser pulse and different switching on functions. In particular, we find that by choosing the laser pulse parameters appropriately the emission of odd harmonics is forbidden and the spectrum contains only even harmonics.

DOI
10.1088/0953-4075/34/18/304

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We find an approximated analytic expression of the acceleration spectrum of a quasi-degenerate two level atom in an external laser field with a non-constant pulse shape function. The spectrum contains odd harmonics and side bands of even harmonics. We show that the relative amplitude of these lines can be controlled by using different rise times of the laser pulse and different switching on functions. In particular, we find that by choosing the laser pulse parameters appropriately the emission of odd harmonics is forbidden and the spectrum contains only even harmonics.
The wave function of a two-level atom driven by a low-frequency laser pulse is obtained in analytical form and is used to determine the power spectrum of the dipole moment of the atom for different initial atomic states. The solution goes over some known approximate solutions and gives the energy of the two dressed states, the position of the hyper-Raman lines, the amplitudes both of the hyper-Raman lines and of the odd harmonics, and the position of the cutoff. The form of the hyper-Raman spectrum results independently of the initial atomic state and shows an onset and a cutoff of the emission.
The acceleration of the electron in a two-level atom driven by a short laser pulse of intermediate strength is calculated and therefore analysed through two wavelet transforms in order to obtain the temporal evolution of the spectrum of the emitted radiation. We show (i) the full spectrum at different instants and (ii) the time profile of some representative harmonics. The growth of the harmonics as well as the appearance and erratic behaviour of the hyper-Raman can be followed with the laser intensity.
The spectrum of a two-level atom in the presence of a multimode laser pulse is calculated. The field is allowed to fluctuate in amplitude or in phase; the emitted spectrum has richer emission lines than in the case of the nonfluctuating field and shows peaks shifted toward the blue with respect to the traditional harmonic peaks. The position of the lines is predicted by the formula ω2n+1=(2n+1)(1+Δ)ωL with Δ being a parameter that can be found numerically. In this way the fluctuations seem to result in an effective increase of the laser frequency.
The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.